<p>Modelling various hazard rate behaviours, particularly non-monotonic patterns, is still a significant challenge in survival and reliability studies. To address these concerns, this paper suggests a novel flexible hazard regression model. The considered approach accommodates a variety of hazards forms, including increasing, decreasing, and bathtub shapes. Several statistical properties are obtained, including the probability density function, hazard rate function, moments, quantile function, order statistics, and stochastic ordering. Four distinct estimation methods are employed to estimate the parameters, and are compared using simulated samples. One practical example illustrates the model’s adaptability and its superior fitting capabilities when compared to existing models. Four regression models within the proportional hazards and parametric frameworks are constructed to account for covariate effects on survival times. To demonstrate the practical applicability of the proposed models, they are applied to primary biliary cirrhosis data and compared with the Cox and parametric regression models. A comprehensive simulation study is conducted to evaluate the probability of correct selection and the mean squared errors of the maximum likelihood estimates of the regression parameters. The proposed hazard regression model thus serves as a flexible and simple alternative to existing survival regression models.</p>